Anomalous Hall crystals in rhombohedral multilayer graphene. II. General mechanism and a minimal model

Soejima, Tomohiro; Dong, Junkai; Wang, Taige; Wang, Tianle; Zaletel, Michael P.; Vishwanath, Ashvin; Parker, Daniel E.

doi:10.1103/physrevb.110.205124

Title: Anomalous Hall crystals in rhombohedral multilayer graphene. II. General mechanism and a minimal model

Journal Article · 12 November 2024 · Physical Review. B

DOI: https://doi.org/10.1103/physrevb.110.205124 · OSTI ID:2481478

^[1];

^[2]; Wang, Tianle ^[3]; Zaletel, Michael P. ^[3]; Vishwanath, Ashvin ^[1];

^[4]

Harvard Univ., Cambridge, MA (United States)
Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States); Univ. of California, Santa Barbara, CA (United States). Kavli Institute for Theoretical Physics
Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Univ. of California, Berkeley, CA (United States); Univ. of California, San Diego, CA (United States)

Here we propose a minimal "three-patch model"for the anomalous Hall crystal (AHC), a topological electronic state that spontaneously breaks both time-reversal symmetry and continuous translation symmetry. The proposal for this state is inspired by the recently observed integer and fractional quantum Hall states in rhombohedral multilayer graphene at zero magnetic field. There, interaction effects appear to amplify the effects of a weak moiré potential, leading to the formation of stable, isolated Chern bands. It has been further shown that Chern bands are stabilized in mean-field calculations even without a moiré potential, enabling a realization of the AHC state. Our model is built on the dissection of the Brillouin zone into patches centered around high-symmetry points. Within this model, the wave functions at high-symmetry points fully determine the topology and energetics of the state. We extract two quantum geometrical phases of the noninteracting wave functions that control the stability of the topologically nontrivial AHC state. The model predicts that the AHC state wins over the topological trivial Wigner crystal in a wide range of parameters, and agrees very well with the results of full self-consistent Hartree-Fock calculations of the rhombohedral multilayer graphene Hamiltonian.

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Research Organization:: Ames Laboratory (AMES), Ames, IA (United States); Energy Frontier Research Centers (EFRC) (United States). Center for Advancement of Topological Semimetals; Gordon and Betty Moore Foundation; Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Organization:: National Science Foundation (NSF); Simons Foundation; USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: AC02-05CH11231; AC02-07CH11358

OSTI ID:: 2481478

Journal Information:: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 20 Vol. 110; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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